1EQQ8ZzGD

• Pooling: certain types (spies in the example) behave like
other types ("pool on the same action"), making it impossible
for the opposite side (the king) to figure out who is
who until one type (usually the "bad" type) reveals himself.
• Building reputation (for credibility, e.g.) and then burning
it at an opportune time.
The study of such models has become a very active area in
game theory. An excellent scholarly monograph on this field
is Repeated Games and Reputations: Long Run Relationships
by George Mailath and Larry Sameulson (http://www.
amazon.com/Repeated-Games-Reptions-Long-Run-Relationships/dp/0195300793/)
— but note that this is an advanced
graduate textbook with lots of math.
A final big-picture remark: in these game-theoretic models,
nobody is actually being tricked. Agents have accurate
beliefs about what the other side is doing (that's the definition
of a nash equilibrium) and are doing the best they can.
Several innovative economic theorists at Stanford (Yossi
Feinberg, Matt Jackson) have remarked that, for this reason,
there isn't really a good model of lying in economics [1]. Real
lying should involve the target being, at least potentially, an
"unsuspecting victim" who really believes what he has been
told. A recent paper that seems to move in this direction is by
ettinger and Jehiel ["A Theory of Deception", American Economic
Journal: Microeconomics 2010, 2(1), pp. 1-20, http://
www.enpc.fr/ceras/jehiel/deception.pdf].
[1] note, for example, that a usual justification for accurate
beliefs in equilibrium is that players have been playing
this kind of game a lot, and have a sense for how often the
truth matches the plain-language meaning of a particular
statement. Maybe that's true when five people have been
playing poker together for a long time. But important lies
are often told "out of equilibrium," when there is no reason
to believe that players have a good "read" of the likelihood
that a claim is true.
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